SOLUTION: ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?

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Question 1045515: ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?
Answer by ikleyn(52786) About Me  (Show Source):
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ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?
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We know AB=CD.

AC=BD=sqrt%285%29.

Perimeter=2AD%2B2AB.

Let AB=x.  Then AD=2x.

You have right angle triangle

x%5E2 + %282x%29%5E2 = %28sqrt%285%29%29%5E2,

5x%5E2=5,

x = 1.

Then AB = 1, AD = 2, and the perimeter = 1 + 2 + 1 + 2 = 6 units.

Answer.  The perimeter is 6 units.

For many other solved similar problems see the lessons
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